Josephson quantum computing device and integrated circuit using such devices

ABSTRACT

A Josephson quantum computing device and an integrated circuit using Josephson quantum computing devices which can realize a NOT gate operation controlled with 2 bits will be provided. The Josephson quantum computing device ( 1 ) comprises: a superconducting ring member ( 10 ) having a π-junction ( 6 ) and a  0 -junction ( 7 ); and a quantum state detecting member ( 20 ) constituted by a superconducting quantum interference device arranged outside of the superconducting ring member, wherein a bonding and an antibonding state brought about by a tunneling effect between a | ↑ &gt; and a | ↓ &gt; state as two states degenerate in energy of the superconducting ring member ( 10 ) are regarded as quantum bits. The bonding and antibonding states as the quantum bits are read out by the quantum state detecting member ( 20 ). The two bit controlled NOT gate operation can be performed by the two quantum bits comprising said quantum bits.

TECHNICAL FIELD

The present invention relates to a Josephson quantum computing deviceutilizing a Josephson device with a π-junction and which can be utilizedin quantum computers, and to an integrated circuit using such computingdevices.

BACKGROUND ART

The quantum computer is a computer that has an overwhelmingly rapidcomputing speed in solving particular problems that could not be solvedin reality by conventional classical computers. In the quantum computer,a quantum two-level system called the quantum bit or qubit is utilizedto correspond to a bit in a classical computer. While a number of qubitsare used in computation, the most basic operation is carried out byunitary transformation manipulations for any one qubit and with aquantum operating device that reads out the qubit manipulated. In asolid-state electronic device, physical states proposed as usable forsuch qubits are superconducting, electronic and nuclear spin states.

At the outset, an explanation is given of basic particulars of qubits.

In general, if there are two physical states corresponding,respectively, to | 0>and | 1>, a state of superposition given by theirsuperposition | 0>+|1> functions as a qubit. Thus, while a classical bitis either 0 or 1, qubits other than | 0> or | 1> state includeinnumerable states intermediate between | 0> and | 1> and further thosewhich are different in phase. It is called unitary transformation to letsuch a certain state | s> change to another state | s′>.

Qubits constituting a quantum computer need to equip the following fourfunctions:

The first is initialization, requiring a means to set an initial stateof a qubit as a well defined one, e. g., | 0> or | 1>.

The second is controlling a state (quantum operating gate), requiring ameans to unitarily transform a prepared initial state (e. g., | 0> or |1>) to any state of superimposition as desired | s>.

The third is to read out, requiring a detecting means to measure aunitarily transformed state | s>, namely to determine the values ofamplitudes of | 0> and | 1>.

The fourth relates to expandability, requiring the conditional statecontrol (controlled NOT gate) first on two bits and then requiringexpansion by integration further to a number of qubits.

As quantum operating devices using superconducting qubits, there is aproposal to utilize electron pair boxes as two superconducting stateshaving different charge states. There is also a proposal to utilize asuperconducting quantum interference device (SQUID) to measuresuperconducting states having states different in phase.

In non-patent references 1 to 3 listed below, a theoretical proposal ofa qubit consisting of a superconducting ring with three Josephsonjunctions and the detection of bonding and antibonding states in theproposed qubit have been reported. In this qubit, if an externalmagnetic field corresponding to half a unit magnetic flux is applied tothe superconducting ring, two states degenerate in energy are realized.As a result, a bonding or an antibonding state that is any arbitrarystate of superposition as desired of the second function mentioned abovefor qubits is formed. In such degenerate states, currents mutuallyopposite in direction flow through the superconducting ring. Thus, thesuperconducting ring to which an external magnetic field near themagnetic field corresponding to one half the unit magnetic flux isapplied is irradiated with a microwave corresponding to an energydifference between the bonding and antibonding states, and asuperconducting quantum interference device disposed around the quantumbit constituted of the superconducting ring is used to indirectlymeasure current flowing through the superconducting ring, therebydetecting if the state is bonding or antibonding.

In non-patent reference 4 in the list below, a theoretical proposal hasbeen made on a qubit using a Josephson junction formed of an anisotropic(d-wave) superconductor and an isotropic (s-wave) superconductor. Inthis Josephson junction, by the effect of the anisotropic (d-wave)superconductor, its free energy becomes the minimum and its systembecomes stable if the phase difference of the superconducting gap is±π/2. The proposed qubit is used to arbitrarily superpose the bondingand antibonding states formed of these two degenerate states as thesecond function mentioned above for qubits.

In non-patent reference 5 in the list below, there have been reported atheoretical proposal on a qubit constituted by a superconducting ringwith one ferromagnetic π-junction and four 0-junction s and reference tothe qubit using an anisotropic superconductor discussed in non-patentreference 3. It is shown that the free energy of this system has itsminimum when the phase difference of the superconducting gap is ±π/2,since the it junction large in the proportion of Josephson function isdisposed between the two pairs of 0-junction s. The proposed qubit isused to arbitrarily superpose the bonding and antibonding states formedof these two degenerate states as the second function mentioned abovefor qubits.

Nonpatent Reference 1: J. E. Mooij and five others, “JosephsonPersistent-Current Qubit”, SCIENCE, vol. 285, pp. 1036 (1999);

Nonpatent Reference 2: Caspar H. van der Wal and seven others, “QuantumSuperposition of Macroscopic Persistent-Current States”, SCIENCE, vol.290, pp. 773 (2000);

Nonpatent Reference 3: I. Chiorescu and three others, “Coherent QuantumDynamics of a Superconducting Flux Qubit”, SCIENCE, vol. 299, pp. 1869(2003);

Nonpatent Reference 4: Lev B. Ioffe and four others, “Environmentallydecoupled sds-wave Josephson junction for quantum computing”, Nature,vol. 398, pp. 679 (1999); and

Nonpatent Reference 5: G. Blatter and two others, “Design aspects ofsuperconducting-phase quantum bits”, Physical Review B, vol. 63, pp.174511-1 (2001).

DISCLOSURE OF THE INVENTION Problems to be Solved by the Invention

In quantum processing devices using a conventional superconducting ringas proposed in nonpatent references 1 to 3 above, however, creating twostates degenerate in energy requires applying thereto an externalmagnetic field corresponding to half a unit magnetic flux. Therefore,the external magnetic field must always be applied to superimposequantum bits.

In quantum processing devices using a conventional superconducting ringas proposed in nonpatent reference 4 above, no current flows through thesuperconducting ring in two degenerate states. Therefore, a circuit mustbe included for joining loops large in inductance for theirdiscriminations.

In quantum processing devices using a conventional superconducting ringas proposed in nonpatent reference 5 above, four 0-junction s and oneπ-junction, namely five Josephson junctions, are required, complicatingthe structure.

Also, in a quantum processing device using a conventionalsuperconducting ring, there is the problem that due to its large size,decoherence can easily be produced. The problem with decoherence is thatquantum states of the quantum processing device are broken by anexternal noise or observation so that the device becomes no longeroperating.

With these problems taken into account, it is a first object of thepresent invention to provide a Josephson quantum computing devicecomprising: a superconducting ring as a quantum bit which with nomagnetic field applied can realize two degenerate states in whichcurrents mutually opposite in direction flow therethrough and which issimple in structure having π and 0-junctions; and a superconductingquantum interference device capable of detecting a quantum state of thesuperconducting ring as the quantum bit.

It is a second object of the present invention to provide a Josephsonquantum computing device comprising: a superconducting ring as a quantumbit which with no magnetic field applied can realize two degeneratestates in which currents mutually opposite in direction flowtherethrough and which is simple in construction having one π- junctionand two 0-junctions; and a superconducting quantum interference devicecapable of detecting a quantum state of the superconducting ring as thequantum bit.

It is a third object of the present invention to provide an integratedcircuit using such Josephson quantum computing devices and which iscapable of performing a NOT logic gating operation controlled by twobits.

Means for Solving the Problems

In order to achieve the first object mentioned above, there is providedin accordance with the present invention a Josephson quantum computingdevice which is characterized in that it comprises: a superconductingring member having a π-junction and a 0-junction; and a quantum statedetecting member constituted by a superconducting quantum interferencedevice arranged outside of the superconducting ring member, wherein abonding and an antibonding state brought about by a tunneling effectbetween a | ↑ > and a | ↓ > state as two states degenerate in energy ofthe superconducting ring member are regarded as quantum bits, and thebonding and antibonding states as the quantum bits are read out by thequantum state detecting member.

Preferably in the structure mentioned above, the superconducting ringmember comprises a pair of semicircular superconductors, a ferromagneticmetal sandwiched between adjacent first ends of the superconductors andan insulator sandwiched between adjacent second ends of thesuperconductors wherein said two superconductors and the ferromagneticmetal together form the π-junction, and the two superconductors and saidinsulator together form said 0-junction . Also, said bonding andantibonding states of the superconducting ring member are preferablycontrolled by a ratio (γ) of Josephson coupling constants at the πand0-junctions.

According to the structure mentioned above, the bonding and antibondingstates as quantum degenerate states can be formed by a superconductingring member with no external magnetic field applied thereto and in asimple construction. When utilized as quantum bits, these two degeneratestates have currents flowing mutually opposite in direction and can thusbe discriminated from each other, which makes it unnecessary to providea separate circuit such as loops.

In the structure mentioned above, the bonding and antibonding states asthe quantum bits are read out by the quantum state detecting memberpreferably upon applying thereto an external magnetic field. Accordingto this structure, the quantum state detecting member is renderedcapable of reading out only upon having a magnetic field appliedthereto.

In the structure mentioned above, the bonding and antibonding states assaid quantum bits are preferably states that they are superposed asdesired by a microwave with which the quantum bits are irradiated.According to this structure, the bonding and antibonding states as thequantum bits can be superposed arbitrarily as desired only when thequantum bits are irradiated with a microwave.

In order to achieve the second object mentioned above, there is providedin accordance with the present invention a Josephson quantum computingdevice which is characterized in that it comprises a superconductingring member having a π-junction and a first and a second 0-junction,each of which is constituted of a Josephson junction, and a quantumstate detecting member constituted by a superconducting quantuminterference device arranged outside of the superconducting ring member,wherein a bonding and an antibonding state brought about by a tunnelingeffect between a | ↑ > and a | ↓ > state as two states degenerate inenergy of the superconducting ring member are regarded as quantum bits,and the bonding and antibonding states as the quantum bits are read outby the quantum state detecting member.

Preferably in the structure mentioned above, the superconducting ringmember comprises a first, a second and a third superconductor which as awhole are disposed in the form of a ring and are strips essentiallytri-partitioned of the ring and arranged having three interspacesbetween their adjacent ends and a ferromagnetic body and a first and asecond insulator with which the three interfaces are filled,respectively, wherein the first superconductor, the first insulator andthe third superconductor together form the first 0-junction; the secondsuperconductor, the second insulator and the third superconductortogether form the second 0 junction; and the first superconductor, theferromagnetic body and the second superconductor together form the it-junction. Also, said bonding and antibonding states of thesuperconducting ring member are preferably controlled by a ratio (γ) ofJosephson coupling constants at the first and second 0-junctions and theπ-junction.

According to the structure mentioned above, the bonding and antibondingstates as quantum degenerate states can be formed by a superconductingring member with. no external magnetic field applied thereto and in asimple construction. When utilized as quantum bits, these two degeneratestates have currents flowing mutually opposite in direction and can thusbe discriminated from each other, which makes it unnecessary to providea separate circuit such as loops.

In the structure mentioned above, the bonding and antibonding states asthe quantum bits are read out by the quantum state detecting memberpreferably upon applying thereto an external magnetic field. Accordingto this structure, the quantum state detecting member is renderedcapable of reading out only upon having a magnetic field appliedthereto.

In the structure mentioned above, the bonding and antibonding states assaid quantum bits are preferably states that they are superposed asdesired by a microwave with which the quantum bits are irradiated.According to this structure, the bonding and antibonding states as thequantum bits can be superposed arbitrarily as desired only when thequantum bits are irradiated with a microwave.

In order to achieve the third object mentioned above, there is providedan integrated circuit which is characterized in that it uses Josephsonquantum computing devices as mentioned above. Preferably, two suchquantum bits adjacent to each other are so arranged as to bring about amagnetic interaction and they are operated as a controlled NOT gate.Also, the bonding and antibonding states as the quantum bits arepreferably states that they are superposed as desired by a microwavewith which the quantum bits are irradiated to operate as a controlledNOT gate.

According to this structure, the NOT gate operation controlled by twobits can be realized by Josephson quantum computing devices according tothe present invention.

Effects of the Invention

According to the Josephson quantum computing device of the presentinvention, quantum bonding and antibonding states which are created bythe superconducting ring member provided with the π-junction and the0-junction can be utilized. These quantum bonding and antibonding statescan be created with no external magnetic field applied. These twodegenerate states in which mutually opposite currents are flowingthrough the superconducting ring member can easily be discriminated fromeach other. Also, quantum bits of the superconducting ring member can bedetected by quantum state detecting member constituted ofsuperconducting quantum interference device disposed around thesuperconducting ring member.

According to the Josephson quantum computing device of the presentinvention, quantum bonding and antibonding states which are created bythe superconducting ring member provided with two 0-junctions and aπ-junction can be utilized. These quantum bonding and antibonding statescan be created with no external magnetic field applied. These twodegenerate states in which mutually opposite currents are flowingthrough the superconducting ring member can easily be discriminated fromeach other. Also, quantum bits of the superconducting ring member can bedetected by the quantum state detecting member constituted ofsuperconducting quantum interference device disposed around thesuperconducting ring member.

According to the present invention, the device having a structureconstituted only of three Josephson junctions can be reduced in size.Consequently, the device can be much less affected by decoherenceattributable to an interaction with its outside.

According to the integrated circuit using Josephson quantum computingdevices of the present invention, it is possible to perform a NOT gateoperation controlled with 2 bits in addition to a 1-bit operation.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings,

FIG. 1 is a plan view diagrammatically illustrating the structure of aJosephson quantum computing device according to the present invention;

FIG. 2 is a diagram illustrating the dependence of total free energy(U₁+U₂+U_(L)) for various γ values when α=7.5×10⁻⁴;

FIG. 3 is a diagram illustrating the dependence of total free energy(U₁+U₂+U_(L)) for various γ values when α=3.6×10⁻¹;

FIG. 4 is a plan view diagrammatically illustrating the structure of aJosephson quantum computing device according to the present invention;

FIG. 5 shows results of computation of total free energy wherein (A) isa contour diagram in a (θ₁, θ₂) space where no external magnetic fieldis applied (Φ_(ext)=0) and (B) is a diagram illustrating the dependenceof U_(tot) on phase space diagonal direction;

FIG. 6 shows results of computation of total free energy where a smallmagnetic flux is applied wherein (A) is a contour diagram in a (θ₁, θ₂)space under an external magnetic field (Φ_(ext) =0.01Φ₀) and (B) is adiagram illustrating the dependence of U_(tot) on phase space diagonaldirection;

FIG. 7 is a plan view diagrammatically illustrating an integratedcircuit using Josephson quantum computing devices according to thepresent invention;

FIG. 8 is a diagrammatic explanatory view illustrating operations of aNOT gate controlled with adjacent two quantum bits in an integratedcircuit using Josephson quantum computing devices according to thepresent invention;

FIG. 9 is a diagrammatic explanatory view illustrating operations of aNOT gate controlled with adjacent two quantum bits in an integratedcircuit using Josephson quantum computing devices according to thepresent invention; and

FIG. 10 is a truth table showing the operations of the NOT gatescontrolled with 2 quantum bits as in FIGS. 8 and 9.

DESCRIPTION OF REFERENCE CHARACTERS

-   1, 30: Josephson quantum computing device-   2, 3, 11, 12: Superconductor-   4, 35: Ferromagnetic metal (F)-   5, 13, 14: Insulator-   6: First junction (π-junction, Josephson junction S1/F/S2)-   7: Second junction (0-junction, Josephson junction S1/I/S2)-   10: Superconducting ring member-   15, 16: Josephson junction in superconducting quantum interference    device-   17, 18, 57, 58: Current terminal-   20, 60: Quantum state detecting member (SQUID)-   32: First superconductor (S1)-   33: Second superconductor (S2)-   34: Third superconductor (S3)-   35: Ferromagnetic metal (F)-   36: Insulator-   37: Insulator-   40: Superconducting ring member-   41: First 0-junction (Josephson junction S1/I₁/S3)-   42: Second 0-junction (Josephson junction S2/I₂/S3)-   43: π-junction (Josephson junction S1/F/S2)-   51, 52: Superconductor-   53, 54: Insulator-   55, 56: Josephson junction in superconducting quantum interference    device-   60: Quantum state detecting member (SQUID)-   70: Integrated circuit using Josephson computing devices-   72: Substrate-   74, 75: Microwave

BEST MODES FOR CARRYING OUT THE INVENTION

Hereinafter, the present invention will be described in detail withreference to certain suitable forms of implementation thereofillustrated in the drawing Figures. In the Figures, the same referencecharacters are used to designate the same or corresponding components.

At the outset, an explanation is given of a first form of implementationof the Josephson quantum computing device according to the presentinvention. FIG. 1 is a diagrammatic plan view illustrating the structureof a Josephson quantum computing device according to the presentinvention. Referring to FIG. 1, the Josephson quantum computing device 1comprises a superconducting ring member 10 with a π- and a 0-junctionand a quantum state detecting member 20 disposed in its outsidecoaxially therewith. The superconducting ring member 10 and the quantumstate detecting member 20 of the Josephson quantum computing device 1can be formed on a substrate. Further, it should be noted that theJosephson quantum computing device operates at a temperature thatexhibits superconductivity.

The superconducting ring member 10 consists of semicircular stripsuperconductors 2 and 3 (hereinafter referred to as S1 and S2 for thesake of convenience) and a ferromagnetic metal 4 (hereinafter referredto conveniently as F) and an insulator 5 (hereinafter referred toconveniently as I) which are sandwiched between the adjacent first endsand the adjacent second ends of the two superconductors 2 and 3,respectively, and is in the form of a ring as a whole. Thesuperconductors 2 and 3 may be superconductors of the same type. Thesuperconducting ring member 10 operates as a Josephson quantum bit. Thesuperconductors 2 and 3 may be Nb, Pb or the like, the ferromagneticmetal 4 may be CuNi, PdNi or the like, and the insulator 5 may be madeof aluminum oxide (AlOx), PbO or the like.

A junction made of superconductor 2 and ferromagnetic metal 4 andsuperconductor 3, namely Josephson junction S1/F/S2 (hereinafterreferred to conveniently as junction 6) is a junction of the firstadjacent ends of the semicircular strip superconductors 2 and 3 with theferromagnetic metal 4 sandwiched between these adjacent ends in contacttherewith. The first junction 6 is a π-junction that becomes stable whenthe phase difference θ between the superconductors 2 and 3 (S1 and S2)is π.

On the other hand, a junction made of the superconductor 2 and theinsulator 5 and the superconductor 3, namely Josephson junction S1/I/S2(hereinafter referred to conveniently as junction 7) is a junction at aposition diagonally opposite to that of the π-junction, namely of thesecond adjacent ends of the semicircular strip superconductors 2 and 3with the insulator 5 (hereinafter referred to conveniently as I)sandwiched between these adjacent ends, that is a tunneling junction.The second junction 7 is a 0 junction that becomes stable when the phasedifference θ′ between the superconductors 2 and 3 (S1 and S2) is 0.

Mention is next made of the quantum state detecting member 20.

The quantum state detecting member 20 is a superconducting quantuminterference device (also called SQUID) having two Josephson junctions.The quantum state detecting member 20 comprises two superconductors 11and 12 which are arranged in the form of a semicircular strip and twoinsulators 13 and 14 sandwiched between the first and second ends ofthem, respectively, to form Josephson junctions 15 and 16. Currentterminals 17 and 18 are disposed at positions 90° spaced from theJosephson junctions 15 and 16. One of the Josephson junctions 15consists of the superconductor 11, the insulator 13, and thesuperconductor 12 and the other Josephson junction 16 is formed from thesuperconductor 11, the insulator 14, and the superconductor 12. Thesuperconductors 11 and 12 may be of the same material as that of thesuperconductors 2 and 3 in the superconducting ring member 10. Also, theinsulators 13 and may be the same in material as the insulator 5 in thesuperconducting ring member 10.

The quantum state detecting member 20 is arranged to read out a quantumstate of the Josephson quantum bit in the superconducting ring member10.

It should be noted further that the superconducting ring member 10 maynot only be circular but also be in the form of a rectangular ring.Then, the quantum state detecting member 20 arranged outside of thesuperconducting ring member 10 may, too, be in the form of a rectangularring similar to the superconducting ring member 10.

The Josephson quantum computing device so constructed as mentioned aboveoperates as described below.

At the outset, an explanation is given of the operation of a quantumbit. The total free energy in the superconducting ring member 10 insideoperating as the quantum bit is expressed by the sum of respectiveelectrostatic energies T₁ and T₂ in the first and second junctions 6 and7, respective Josephson energies U₁ and U₂ in the first and secondjunctions 6 and 7 and magnetic energy U_(L) stored in thesuperconducting ring member 10. Behaviors of this system correspond tomotions of a particle with kinetic energy T₂ in potential U₁+U₂+U_(L).

The electrostatic energy in the first junction 6 is expressed by T₁=Q₁²/2C₁. Likewise, the electrostatic energy in the second junction 7 isexpressed by T₂=Q₂ ²/2C₂. Here, Q₁ and Q₂ are charges stored at thefirst and second junctions 6 and 7, respectively. C₁ and C₂ areelectrostatic capacitances at the first and second junctions 6 and 7,respectively.

The electrostatic energy T₁ at the first junction 6 that is of metalcontact as being a metallic junction is much smaller than theelectrostatic energy T₂ at the second junction 7 sandwiching theinsulator film 5 and is negligible (T₁<<T₂). Also, the superconductingcritical current I_(π) at the first junction 6 which is a π-junction ofmetal contact is expressed by equation (1) below.

Iπ=2eE _(π)/  (1)

where e is the elementary electric charge and  is the Planck constantdivided by 2π. And, E_(π) is the coupling constant representing thestrength of Josephson junction.

Using the coupling constant E_(π), the Josephson coupling energy isexpressed by U₁=−E_(π)|cos((θ+π)/2)|.

On the other hand, the superconducting critical current I₀ at the secondjunction 7 which is a normal Josephson junction sandwiching theinsulator 5 is expressed by equation (2) below.

I ₀=2eE ₀/  (2)

where E₀ is the Josephson coupling constant, and the binding energy atthe second junction 7 is expressed by U₂=−E₀cos θ′.

The Josephson energy U₂ at the second junction 7 can be expressed as afunction of θ, since there is a relation θ−θ′=2πΦ/Φ₀ (where Φ₀ is theunit magnetic flux; Φ₀=h/2e=2.086×10⁻¹⁵ Wb) between phase differences θand θ′ of the first and second junctions 6 and 7 through magnetic flux Φpassing the inside of the superconducting ring member 10. Note here thatthe ratio of Josephson coupling constants at the first and secondjunctions 6 and 7 is assumed to be γ=E₉₀/E₀.

Further, the magnetic energy U_(L) stored in the superconducting ringmember 10 is expressed by U_(L)=(Φ−Φ_(ext))²/2L. Here, L is a selfinductance and Φ_(ext) is an externally applied magnetic flux. There isintroduced α=2πLI₀Φ₀ as a dimensionless parameter representing themagnitude of self inductance.

Results of computation of the total free energy in the superconductingring member 10 operating as quantum bits are explained.

FIG. 2 is a diagram illustrating the dependence of the total free energy(U₁+U₂+U_(L)) for various γ values when α=7.5×10⁻⁴. The state here is,however, where no external magnetic flux is applied (Φ_(ext)=0). Thevalue of α corresponds to where the radius of the superconducting ringmember 10: r=5 μm, the cross section of the junction surfaces: S=10⁻²μm² and the thickness of the insulator in the second junction 7: d=1 nm.In FIG. 2, the abscissa axis represents the phase θ (π radian) of thesecond junction 7 and the ordinate axis represents the total free energyof the second junction 7 normalized by Josephson coupling constant E₀((U₁+U₂+U_(L))/E₀; this energy is called “normalized total freeenergy”).

If the ratio γ(=E_(π)/E₀) of the Josephson coupling constants at thefirst and second junctions 6 and 7 is incrementally increased by 0.5from 2 to 3.5, the normalized total free energy ((U₁+U₂+U_(L))/E₀)varies with the phase θ of the second junction 7. As can be seen fromFIG. 2, where γ is around 2 to 3, the normalized total free energy hasthe two minimum values degenerate in energy and the θ corresponding tothem is the phase difference that is realized.

FIG. 3 is a diagram illustrating the dependence of the total free energy(U₁+U₂+U_(L)) for various y values when α=3.6×10⁻¹. The state here is,however, where no external magnetic flux is applied (Φ_(ext)=0). Theabscissa and ordinate axes in the Figure are the same as those in FIG.2. The value of α corresponds to where the radius of the superconductingring member 10: r=1 mm, the cross section of the junction surfaces:S=10⁻² μm² and the thickness of the insulator in the second junction 7:d=1 nm.

If the ratio γ(=E_(π)/E₀) of the Josephson coupling constants at thefirst and second junctions 6 and 7 is incrementally increased by 1 from2 to 5, the normalized total free energy varies with the phase θ of thesecond junction 7. As can be seen from FIG. 3, where γ is around 2 to 4,the normalized total free energy has the two minimum values degeneratein energy and the θ corresponding to them is the phase difference thatis realized.

In FIGS. 2 and 3, the two minimum values degenerate in energy become thetwo stable states. Let these two stable states to be | ↑ > and | ↓ >. Inthe states | ↑ > and | ↓ >, electric currents of the same magnitude areflowing in mutually opposite directions through the superconducting ringmember 10, and magnetic fluxes of the same magnitude and in mutuallyopposite directions corresponding thereto enter the superconducting ringmember 10. The magnitude of currents then flowing in the states | ↑ >and | ↓ > become | I| ˜ | I₀ |˜10⁻² μ A in both FIGS. 2 and 3. Themagnitude of the magnetic fluxes passing through the superconductingring member 10 becomes | Φ | ˜2.1×10⁻¹⁹ Wb (γ=3) with FIGS. 2 and1.0×10⁻¹⁶ Wb (γ=3) with FIG. 3.

The electrostatic energy in the second junction 7 becomes T₂˜6.8×10⁻²³ Jif alumina (Al₂O₃) of a dielectric constant: k˜8.5 is used as theinsulator 5. Since this value of electrostatic energy T₂ is close in theorder to the Josephson coupling constant E₀˜3.3×10⁻²⁴ J, a tunnelingeffect is brought about between the | ↑ > and | ↓ > as the two statesdegenerate in energy with the result that the bonding and antibondingstates in which | ↑ 22 and | ↓ > are superposed appear. Here, thebonding state: | 0> is expressed as | 0> ∝ | ↑ > + | ↓ > and is theground state. The antibonding state: | 1> is expressed as | 1> ∝ | ↑ > −| ↓ > and is the excited state.

Therefore, in the superconducting ring member 10 according to thepresent invention, the bonding state bit: | 0> = | ↑ > + | ↓ > and theantibonding state bit: | 1> = | ↑ > − | ↓ > are utilized as quantumbits.

As an energy gap ΔE exists between the bonding and antibonding states,it is possible to irradiate a quantum bit with a microwave angularfrequency: ω=Δ E/h (h: Planck constant) corresponding to the gap and toobserve its resonance absorption and thereby to check the presence ofthe bonding or antibonding state. The frequency corresponding to the gap(f=ω/2π) is found to be around several GHz by various constants used incomputation of the total free energy shown in FIG. 2.

Thus, it is seen that the bonding and antibonding states can be realizedby the quantum bits consisting of one π-junction and one 0-junction ,two in total, of the superconducting ring member 10 in which conditionssuch as the electrostatic energy T₂, the Josephson coupling constant E₀and γ are appropriately selected. And, these bonding and antibondingstates can be realized with no external magnetic field applied. Further,since in the two states degenerated, currents directed mutually oppositeare passed through the superconducting ring member 10, they are easy todiscriminate. Since the quantum bit according to the present inventionconsists of 2 junctions, the structure is simple. They are easy tomanufacture, accordingly.

The two stable states to be brought about in the superconducting ringmember 10 and the bonding and antibonding states can be effected at thesame time. On the other hand, the superconducting ring member 10 can beinitialized as follows. Namely, if it is kept at low temperaturesufficient so that thermal excitation from the bonding state | 0> thatis a ground state to the antibonding state | 1> that is an excitationstate may not occur, it can be relaxed to the ground state and hence beinitialized to the bonding state | 0>.

Further, in the case of exciting from the bonding state |0> of thesuperconducting ring member 10 to its antibonding state | 1>, if thesuperconducting ring member 10 is irradiated with a microwave of afrequency corresponding to the energy gap Δ E_(B1) which is when thesuperconducting ring member 10 is in the state | 1> its state can beexcited from the bonding state | 0> to the antibonding state | 1>.

Next, the readout operations of the bonding and antibonding states ofthe quantum bit will be explained. The bonding and antibonding states ofthe quantum bit of the superconducting ring member 10 are read out bythe superconducting quantum interference device of the quantum statedetecting member 20 disposed around the Josephson quantum bit of thesuperconducting ring member 10. In this case, a bias current is appliedbetween current terminals 17 and in the superconducting quantuminterference device of the quantum state detecting member 20 and a valueof current (switching current), which gives rise to a finite voltagewhen the current is increased, is measured for readout.

Here, mention is made of where no external magnetic flux is applied(Φ_(ext)=0). Zero magnetic flux will be detected as an anticipated valuewhen the quantum bit is in the bonding or antibonding state, since inthe degenerate | ↑ > and | ↓ > states, magnetic fluxes mutually oppositein direction enter the superconducting ring member 10.

On the other hand, since an asymmetry in θ dependence of the potentialoccurs when a small external magnetic flux is applied (Φ_(ext)≠0), afinite flux is detected in the bonding and antibonding states as well.This allows the bonding and antibonding states of the quantum bits ofthe superconducting ring member 10 to be read out by making a fluxmeasurement with the superconducting quantum interference device of thequantum state detecting member 20 while changing the external magneticflux in the vicinity of zero.

As described above, the Josephson quantum computing device 1 accordingto the present invention allows the functions to initialize, to controlthe state and to read out to be realized with Josephson quantum bits bythe superconducting ring member 10 with π- and 0-junctions and thequantum state detecting member 20.

The Josephson quantum computing device of the present inventionconstructed as mentioned above can be fabricated as described below.

First, a superconductor becoming the superconducting ring member 10 andthe quantum state detecting member 20 is deposited by sputtering onto aninsulating substrate to a selected thickness. Then, the superconductingring member 10 and the ring of quantum state detecting member 20 areformed by selective etching process with mask. The superconductor atthose areas of the ferromagnetic metal 4 and the insulator 5 of thesuperconducting ring member 10 and the insulators 13 and 14 of thequantum state detecting member 20 is etched, too.

Next, an insulating material such as aluminum oxide becoming theinsulators 5, 13 and 14 is deposited by sputtering or CVD method to aselected thickness. And, excess portions of the insulating material areremoved by selective etching. In this process step, the 0-junction 7 andthe quantum state detecting member 20 are formed.

Finally, a film of the ferromagnetic metal 4 is deposited by sputteringto a selected thickness. And, an excess portion of the ferromagneticmetal film is removed by selective etching. In this process step, theπ-junction 6 is formed. In depositing each material, an ordinary thinfilm forming method such as vapor deposition, laser ablation or MBEother than sputtering or CVD may be used. Also, in masking steps forforming junctions and current terminals of selected shapes, photo orelectron beam exposure may be used.

A second form of implementation of the Josephson quantum computingdevice according to the present invention will be explained.

FIG. 4 is a plan view diagrammatically illustrating the structure of aJosephson quantum computing device 30 according to the presentinvention. As shown, the Josephson quantum computing device 30 accordingto the present invention comprises a superconducting ring member 40 withtwo 0-junctions 41 and 42 and one π-junction 43 each of which is aJosephson junction and a quantum state detecting member 60 arrangedoutside of the superconducting ring member 40 coaxially therewith. Thesuperconducting ring member 40 and the quantum state detecting member 60of the Josephson quantum computing device 30 may be formed on asubstrate. It should be noted here that the Josephson quantum computingdevice of the present invention operates at a temperature at whichsuperconductivity is exhibited.

The superconducting ring member 40 comprises a first, a second and athird superconductor 32, 33 and 34 clockwise (hereinafter referred toconveniently as S1, S2 and S3, respectively) which as a whole aredisposed in the form of a ring and are strips essentiallytri-partitioned of the ring and arranged having three interspaces openbetween their adjacent ends and a ferromagnetic metal 35 (hereinafterreferred to conveniently as F) and a first and a second insulator 36 and37 (hereinafter referred to conveniently as I₁ and I₂, respectively)with which the three interfaces are filled, respectively.

The ferromagnetic metal 35 is arranged sandwiched between the adjacentends of the first and second superconductors 32 and 33. The firstinsulator 36 is arranged sandwiched between the adjacent ends of thefirst and third superconductors 32 and 34. The second insulator 37 isarranged sandwiched between the adjacent ends of the second and thirdsuperconductors 33 and 34. The first to third superconductors 32, 33 and34 may be of an identical superconducting material. The first and secondinsulators 36 and 37 may be of an identical insulating material. Thesuperconducting ring member 40 operates as a Josephson quantum bit. Thefirst to third superconductors 32, 33 and 34 used may be of Nb, Pb orthe like, the ferromagnetic metal 35 used may be of CuNi, PdNi or thelike, and the first and second insulators 36 and 37 used may be ofaluminum oxide (AlOx), PbO or the like.

The first 0-junction 41 is a Josephson junction made of the firstsuperconductor 32, the first insulator 36 and the third superconductor34. The first 0-junction S1/I₁/S3 is a tunneling junction made of theadjacent ends of the first and third strip superconductors 32 and 34that are substantially tri-partitions of the circle and the firstinsulator 36 sandwiched between these ends. The first 0-junction 41 is a0-junction that becomes stable if the phase difference θ₁ between S1 andI₁ and S3 forming the 0-junction is zero.

The second 0-junction 42 is a Josephson junction made of the secondsuperconductor 33, the second insulator 37 and the third superconductor34. The second 0-junction S2/I₂/S3 is a tunneling junction made of theadjacent ends of the second and third strip superconductors 33 and 34that are substantially tri-partitions of the circle and the secondinsulator 37 sandwiched between these ends. The second 0-junction 42 isa 0-junction that becomes stable if the phase difference θ₂ between S2and I₂ and S3 forming the 0-junction is zero.

On the other hand, the π-junction 43 is a Josephson junction made of thefirst superconductor 32, the ferromagnetic body 35 and the secondsuperconductor 33. That is, the π-unction S1/F/S2 is a tunnelingjunction made of the adjacent ends of the first and second stripsuperconductors 32 and 33 that are substantially tri-partitions of thecircle and the ferromagnetic body 35 sandwiched between these ends. Theπ-junction 43 is a π-junction that becomes stable if the phasedifference θ₃ between S1 and F and S2 forming the π-junction is π.

The quantum state detecting member 60 will be explained next. Thequantum state detecting member 60 comprises a so called superconductingquantum interference device having a pair of Josephson junctions. Thequantum state detecting member 60 has semicircular superconductors 51and 52 arranged in the form of a ring and insulators 53 and 54sandwiched between their respective and adjacent ends to form Josephsonjunctions 55 and 56. Current terminals 57 and 58 are provided atpositions spaced by about an angle of 90° from the Josephson junctions55 and 56.

One Josephson junction 55 is formed of the superconductor 51, theinsulator 53 and the superconductor 52 while the other Josephsonjunction 56 is formed of the superconductor 51, the insulator 54 and thesuperconductor 52.

Here, the superconductors 51 and 52 may be of a same material as that ofthe first, second and third superconductors 32, 33 and 34 of thesuperconducting ring member 40. The insulators 53 and 54 may be of asame material as that of the first and second insulators 36 and 37 ofthe superconducting ring member 40. The insulator 53 of the quantumstate detecting member 60 is arranged opposed to the ferromagnetic body35 of the superconducting ring member 40.

The quantum state detecting member 60 is disposed to read out a quantumstate of the Josephson quantum bit in the superconducting ring member40.

Here, it should be noted further that the superconducting ring member 40may not only be circular but also be a square ring. Then, the quantumstate detecting member 60 disposed outside of the superconducting ringmember 40 may be a square ring similar to the superconducting ringmember 40.

An explanation is next given of operations of the Josephson quantumcomputing device according to the present invention constructed asmentioned above.

At the beginning, the quantum bit will be mentioned. The total feeenergy in the quantum bit is expressed as a sum of electrostaticenergies K₁, K₂ and K₃, Josephson coupling energies U₁, U₂ and U₃ at thefirst and second 0-junctions and π-junction 41, 42 and 43, and themagnetic energy U_(L) stored in the superconducting ring.

First, the electrostatic energy at the first 0-junction 41 is expressedas K₁=Q₁ ²/2C₁. Likewise, the electrostatic energy at the second0-junction 42 is expressed as K₂=Q₂ ²/2C₂, and electrostatic energy atthe π-junction 43 as K₃=Q₃ ²/2C₃. Each of these electrostatic energiescorresponds to the kinetic energy in the phase space. Q₁, Q₂ and Q₃ arecharges stored at the first and second 0-junctions 41 and 42 and theπ-junction 43. C₁, C₂ and C₃ are capacitances of the junctions 41, 42and 43.

Next, the binding energies of the first and second 0-junctions areexpressed as U₁=−E₀ cos θ₁ and U₂=−E₀ cos θ₂, respectively. Here, E₀ isthe Josephson coupling constant, and the Josephson coupling constant atthe second 0-junction 42 is regarded as being equal to that at the first0-junction 41.

The Josephson binding energy at the π-junction 43 is expressed as U₃=−E₃cos(θ₃+π) where E₃ is the Josephson coupling constant. The ratio of theJosephson constants at the 0-junctions 41, 42 and π-junction 43 isconsidered as γ=E₃ /E₀.

With respect to total magnetic flux Φ passing through thesuperconducting ring member 40, the magnetic energy U_(L) stored in thesuperconducting ring member 40 is expressed as U_(L)=(Φ−Φ_(ext))²/2L.Here, L is a self inductance and Φ_(ext) is a magnetic flux externallyapplied. And, α=4π²E₃L/Φ₀ ² is introduced where Φ₀ is a unit magneticflux as a dimensionless parameter that represents the self inductance.

Mention is next made of the total free energy at the superconductingring member 40 operating as the quantum bit. Total free energy U_(tot)is expressed as U_(tot)=U₁+U₂+U₃+U_(L) and as a function of fourvariables (θ₁, θ₂, θ₃, Φ). The total free energy becomes a function oftwo variables (θ₁, θ₂) from relations that θ₁+θ₂+θ₃=2πΦ/Φ₀ which standsbetween the superconducting phase and total magnetic flux, and thecondition (U_(tot)/Φ=0) under which the total free energy for totalmagnetic flux Φ becomes the minimum.

FIG. 5 shows results of computation of the total free energy wherein (A)is contour diagram in a (θ₁, θ₂) space where no external magnetic fieldis applied (Φ_(ext)=0) and (B) is a diagram illustrating the dependenceof U_(tot) phase space on diagonal direction. In FIG. 5(A), the abscissaaxis represents θ₁ which is normalized with π and the ordinatesrepresents θ₂ which is normalized with π. In FIG. 5(B), the abscissaaxis represents θ₁ and θ₂ in diagonal direction which are normalizedwith πand the ordinates represents U_(tot) which is normalized with E₀.The value of α corresponds to the case that r=1 μm, S=0.1 μm and d=1 nmwhere r is the ring radius of the superconducting ring member 40, S isthe cross sectional area of junction surfaces of the first and second0-junctions and the π-junction 41, 42 and 43, and d is the thickness ofthe insulators and is that α=3.1×10⁻³. Also, it applies that γ=0.8.

As is apparent from FIG. 5, it is seen that centering on coordinates (2nπ and 2m π where n and m are each an arbitrary integer) in the phasespace, there are found two minimum values degenerate in their respectivediagonal directions. Stable states in energy by these two degenerateminimum values are realized in the superconducting ring member 40. And,θ₁ and θ₂ which correspond to the two minimum values degenerate indiagonal directions are the phase differences which are realized.

In FIG. 5, the two minimum values degenerate in energy become the twostable states. These two stable states are regarded as | ↑ > and | ↓ >.In the states | ↑ > and | ↓ >, currents of a same magnitude and mutuallyopposite in direction flow in the superconducting ring member 40, andcorrespondingly thereto, magnetic fluxes of a same magnitude andmutually opposite in direction pass through the superconducting ringmember 40. The magnitude of the fluxes is that | Φ | ≈ 4.8×10⁻⁴ Φ₀˜10⁻¹⁸Wb.

In the case of FIG. 5, if alumina (Al₂O₃; dielectric constant κ˜8.5) isused for the insulators 36 and 37 in the first and second 0-junction s41 and 42, electrostatic energy per single electron, namely singleelectron Coulomb energy: E_(C)=e²/2C_(1,2) (where e is elementarycharge) then has the value of E_(C)˜1.7−10²⁴ J. Also, using a typicalvalue I₀˜500 nA of the Josephson critical current at the first andsecond 0-junctions 41 and 42, Josephson coupling constant E₀=1.6×10⁻²² Jis obtained.

As for the single electron Coulomb energy E_(C) and the electrostaticenergy, there exists relation: K=Q²/2C=(ne)²/2C=n²E_(C) where n is thenumber of electrons at each junction.

The value 1.7×10⁻²⁴ J of the electrostatic energy E_(C) becomes close inthe order to the value 1.6×10⁻²² J of Josephson coupling constant E₀.This causes the effect of electrostatic energy corresponding to kineticenergy in the phase space to bring about a tunneling effect between twostates, | ↑ > and | ↓ >, degenerate in energy in the superconductingring member 40, thereby developing the bonding and antibonding states inwhich | ↑ > and | ↓ > are superimposed. Here, the bonding state: | 0> isexpressed by | 0> ∝ | ↑ > + | ↓ > and is a ground state. The antibondingstate |1> is expressed by | 1> ∝ | ↑ > − | ↓ >, and is an excitationstate.

Thus, the bonding state | 0> = | ↑ > + | ↓ > and the antibonding state |1> = | ↑ > − | ↓ > are utilized for bits in the superconducting ringmember 40 as quantum bits. Therefore, the bonding and antibonding statescan be realized by the quantum bit constituted of one π junction and two0 junctions, that is, Josephson junctions 41, 42, 43 three in total ofthe superconducting ring member 40 in which conditions such aselectrostatic energies K₁, K₂ and K₃, Josephson coupling constant E₀ andγ are appropriately chosen.

Since an energy gap Δ E exists between the bonding and antibondingstates, the presence of the bonding or antibonding state can beascertained by irradiating the quantum bit with a microwave havingangular frequency ω=Δ E/h (where h is the Planck constant) whichcorresponds to the gap and observing its resonance absorption. Thefrequency (f=ω/2π) corresponding to the gap becomes around several GHzfrom various constants for use. in computation of the total free energyshown in FIG. 5.

The bonding and antibonding states can be realized without applyingexternal magnetic field. Further, in two degenerate states, sincecurrents mutually opposite in direction flow through the superconductingring member 40, they are easy to discriminate. Since the quantum bitaccording to the present invention is constituted of only threejunctions, its structure is simple and the device can be reduced insize. Thus, the decoherence is hard to occur. Also, the device can bemanufactured easily.

The two stable states in the superconducting ring member 40 and thebonding and antibonding states to be brought about can be realized atthe same time. On the other hand, the superconducting ring member 40 canbe initialized as follows. Namely, when it is kept at low temperaturesufficient so that the thermal excitation from the bonding state | 0>,which is a ground state, to the antibonding state | 1>, which is anexcitation state, may not occur, it can be relaxed to the ground stateand hence be initialized to the bonding state | 0>.

In the case of exciting from the bonding state | 0> of thesuperconducting ring member 40 to its antibonding state | 1>, if thesuperconducting ring member 40 is irradiated with a microwave of afrequency corresponding to the energy gap ΔE_(C1) which is when thesuperconducting ring member 40 is in the state | 1>its state can beexcited from the bonding state | 0> to the antibonding state | 1>.

Next, the readout operations of the bonding and antibonding states ofthe quantum bit will be explained. The bonding and antibonding states ofthe quantum bit of the superconducting ring member 40 are read out bythe superconducting quantum interference device of the quantum statedetecting member 60 disposed around the Josephson quantum bit of thesuperconducting ring member 40. In this case, a bias current is appliedbetween current terminals 57 and in the superconducting quantuminterference device of the quantum state detecting member 60. A value ofcurrent (switching current), which gives rise to a finite voltage whenthe current is increased, is measured for readout.

Here, the mention is made of where no external magnetic flux is applied(Φ_(ext)=0).

The zero magnetic flux will be detected as an anticipated value when thequantum bit is in the bonding or antibonding state, since magneticfluxes mutually opposite in direction enter to the superconducting ringmember 40 in the degenerated | ↑ > and | ↓ > states.

On the other hand, since an asymmetry in θ dependence of the potentialoccurs when a small magnetic flux is applied (Φ_(ext)≠0), a finite fluxis detected in the bonding and antibonding states as well. FIG. 6 showsresults of computation of the total free energy where a small magneticflux is applied wherein (A) is a contour diagram in a (θ₁, θ₂) spaceunder an external magnetic field (Φ_(ext)=0.01Φ₀) and (B) is a diagramillustrating the dependence of U_(tot) on phase space diagonaldirection. The values of various parameters other than the externalmagnetic field are the same as in FIG. 5. As is apparent from FIG. 6,applying a magnetic field relieves the states | ↑ > and | ↓ > fromdegeneration to bring about an asymmetry of potential in diagonaldirection centering on the coordinate (2n π, 2m π). As a result,currents flowing turning in mutually opposite directions through thesuperconducting ring in the bonding and antibonding states make itpossible to discriminate the states of the quantum bit with the SQUIDdetector. Thus, it is possible to read out the bonding and antibondingstates of the quantum bit in the superconducting ring member 40 byvarying the external magnetic field in the vicinity of zero while makinga flux measurement with the superconducting quantum interference deviceof the quantum state detecting member 60.

An operation with Josephson quantum computing devices according to thepresent invention will be explained. It is necessary to realize one-bitoperations and a two-bit controlled NOT logic operation (hereinafter,also referred to as controlled NOT gating) in order to construct auniversal circuit using quantum bits according to Josephson quantumcomputing devices 1 or 30 of the present invention.

First, as for a one-bit operation, any state of superposition can berealized in oscillations (Rabi oscillations) between the bonding andantibonding states using microwave resonance by adjusting the pulsewidth of the microwave.

A two-bit controlled NOT gating can be realized using quantum bitsaccording to Josephson quantum computing devices 1 or 30 of the presentinvention as stated below.

Mention is first made of an integrated circuit with Josephson quantumcomputing devices 1, 30 of the present invention. FIG. 7 is a plan viewdiagrammatically illustrating an integrated circuit 70 using Josephsonquantum computing devices according to the present invention. In theFigure, the integrated circuit 70 using Josephson quantum computingdevices 30 is formed as the matrix configuration on a substrate 72 withthe Josephson quantum computing devices 30 of the present invention. Thesubstrate 72 used may be an insulating substrate. While the Josephsonquantum computing devices are shown as 30A-30P, they may be Josephsonquantum computing devices 1A-1P. The number of devices may arbitrarilybe set as desired. Two adjacent quantum bits of the Josephson quantumcomputing devices 30A-30P are arranged spaced apart at a distance suchthat they are affected each other by their mutual magnetic interaction.

Mention is next made of the NOT gating controlled by adjacent twoquantum bits in the integrated circuit 70 using the Josephson quantumcomputing devices 1, 30 of the present invention. FIG. 8 is anexplanatory view diagrammatically illustrating operations of a NOT gatecontrolled with adjacent two quantum bits in an integrated circuit usingJosephson quantum computing devices 1 according to the presentinvention. As shown, adjacent quantum bits 1A and 1B are arranged spacedapart at a distance (see the two-headed arrow in FIG. 8) such that theyare affected each other by their mutual magnetic interaction. Here, thequantum bits 1A and 1B have their superconducting ring members shown andtheir quantum state detecting members are omitted.

The quantum bits 1A and 1B play their respective roles as a control anda target quantum bit. For a magnetic interaction between quantum bits 1Aand 1B, the energy gap in target quantum bit 1B depends on the state ofcontrol quantum bit 1A. More specifically, the current flowing throughthe quantum bit 1A gives the quantum bit 1B an effective external fluxthrough their mutual inductance. Since the orientation of this effectiveexternal magnetic flux depends on the orientation of the current throughthe quantum bit 1A, the magnitude of the total external magnetic fluxapplied to the quantum bit 1B depends on the state of the quantum bit1A.

Consider that the energy gaps of the quantum bit 1B if the controlquantum bit 1A is in the state | 0> and in the state | 1> are Δ E_(B0)and Δ E_(B1), respectively. When this target quantum bit 1B isirradiated with a microwave 74 of a frequency corresponding to Δ E_(B1),the target quantum bit 1B changes its state only when the controlquantum bit 1A is in the state |1>. In this way, a NOT gate controlledby two of Josephson quantum computing devices 1 is realized.

FIG. 9 is an explanatory view diagrammatically illustrating operationsof the NOT gate controlled with adjacent two quantum bits in theintegrated circuit using Josephson quantum computing devices 30according to the present invention. As shown, adjacent quantum bits 30Aand 30B are arranged spaced apart at a distance (see the two-headedarrow in FIG. 9) such that they are affected each other by their mutualmagnetic interaction. Here, the quantum bits 30A and 30B have theirsuperconducting ring members shown and their quantum state detectingmembers are omitted.

In the above quantum bits, the quantum bits 30A plays role as a controlbit and the quantum bits 30B plays role as a target bit. For a magneticinteraction between quantum bits 30A and 30B, the energy gap in targetquantum bit 30B depends on the state of control quantum bit 30A. Morespecifically, the current flowing through the quantum bit 30A gives thequantum bit 30B an effective external flux through their mutualinductance. Since the orientation of this effective external magneticflux depends on the orientation of the current through the quantum bit30A, the magnitude of the total external magnetic flux applied to thequantum bit 30B depends on the state of the quantum bit 30A.

Consider that the energy gaps of the quantum bit 30B if the controlquantum bit 30A is in the state | 0> and in the state | 1> are Δ E_(C0)and Δ E_(C1), respectively. When this target quantum bit 30B isirradiated with a microwave 75 of a frequency corresponding to Δ E_(C1),the target quantum bit 30B changes its state only when the controlquantum bit 30A is in the state | 1>. In this way, a NOT gate controlledby two of Josephson quantum computing devices 30 is realized as in thecase that two Josephson quantum computing devices 1 are used.

FIG. 10 is a truth table showing the operations of the NOT gatescontrolled with 2 quantum bits as in FIGS. 8 and 9. As is shown, whenthe input control quantum bit 1A (30A) is in the state | 1>, it ispossible to change the output of the target quantum bit 1B (30B) fromthe state | 1> to the state | 0> or from the state | 0> to the state |1>. Then, the state of the target quantum bit 1B (30B) can be changedfrom the state | 0> to the state | 1> or from the state | 1> to thestate | 0> can be changed by irradiating the target quantum bit 1B (30B)with a microwave of a frequency corresponding to Δ E_(B1) (Δ E_(C1)) andeffecting a Rabi oscillation between the bonding and antibonding statesusing the resonance. Here, the microwave irradiation can be adjusted byvarying its pulse width or frequency. Thus, the operations of acontrolled NOT gate can be realized according to 2 quantum bits usingtwo of Josephson quantum computing devices 1 or Josephson quantumdevices 30.

The Josephson quantum computing device 30 and the integrated circuitwith such devices according to the present invention can be manufacturedas stated below.

First, a superconductor becoming the superconducting ring member 40 andthe quantum state detecting member 60 is deposited by sputtering to aselected thickness. Then, the superconducting ring member 40 and thering of quantum state detecting member 60 are formed by selectiveetching with mask. The superconductor at those areas of theferromagnetic metal 35 and the insulators 36 and 37 of thesuperconducting ring member 40 and the insulators 53 and 54 of thequantum state detecting member 60 is etched, too.

Next, an insulating material such as aluminum oxide becoming theinsulators 36, 37, 53 and 54 is deposited by sputtering or CVD method toa selected thickness. And, excess portions of the insulator material areremoved by selective etching. In this process step, the first and second0-junctions 41 and 42 of the superconducting ring member 40 and thequantum state detecting member 60 are formed.

Finally, a film of the ferromagnetic metal 35 is deposited by sputteringto a selected thickness. And, an excess portion of the ferromagneticmetal film 35 is removed by selective etching. In this process step, theπ-junction 43 in the superconducting ring member 40 is formed. Indepositing each material, an ordinary thin film forming method such asvapor deposition, laser ablation or MBE other than sputtering or CVD maybe used. Also, in masking steps for forming junctions and currentterminals of selected shapes, photo or electron beam exposure may beused.

The present invention is not limited to these specific examples andallows various modifications thereof to be made within the scope of theinvention set forth in the appended claims, and it is a matter of coursethat these modifications as well fall in the scope of the presentinvention.

1-8. (canceled)
 9. A Josephson quantum computing device, characterizedin that it comprises: a superconducting ring member having a first and asecond 0-junction and a π-junction each of which is constituted of aJosephson junction; and a quantum state detecting member constituted bya superconducting quantum interference device arranged outside of saidsuperconducting ring member, wherein: a bonding and an antibonding statebrought about by a tunneling effect between a |↑> and a |↓> state as twostates degenerate in energy of said superconducting ring member areregarded as quantum bits, and said bonding and antibonding states as thequantum bits are read out by said quantum state detecting member. 10.The Josephson quantum computing device as set forth in claim 9,characterized in that: said superconducting ring member comprises afirst, a second and a third superconductor which as a whole are disposedin the form of a ring and are strips essentially tri-partitioned of thering and arranged having three interspaces open between their adjacentends and a ferromagnetic body and a first and a second insulator withwhich the three interfaces are filled, respectively, wherein: said firstsuperconductor, said first insulator and said third superconductortogether form said first 0-junction, said second superconductor, saidsecond insulator and said third superconductor together form said second0 junction, and said first superconductor, said ferromagnetic body andsaid second superconductor together form said π-junction.
 11. TheJosephson quantum computing device as set forth in claim 9,characterized in that said bonding and antibonding states of saidsuperconducting ring member are controlled by a ratio (γ) of Josephsoncoupling constants at said first and second 0-junctions and saidπ-junction.
 12. The Josephson quantum computing device as set forth inclaim 9, characterized in that said bonding and antibonding states asthe quantum bits are read out by said quantum state detecting memberupon applying thereto an external magnetic field.
 13. The Josephsonquantum computing device as set forth in claim 9, characterized in thatsaid bonding and antibonding states as the quantum bits are states thatare superposed arbitrarily as desired by a microwave with which saidquantum bits are irradiated. 14-20. (canceled)